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shashi598

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These are questions asked by shashi598

I recently got introduced to fractional calculus, I saw this image on the internet and went to verify the 3rd block of image i.e fractional differentiation on Maple 2022. But Maple returned answer which does not match the result claimed in the image i.e x. I want to know what I am missing here. But when used fracdiff() the answer matches.I also wanted to know how its done by using showSolution command but didn't get the answer. Can I get the steps? meme.mw


f := diff(x, [`$`(x, 1/2)])

x

(1)

``

evalb(diff(x, [`$`(x, 1/2)]) = x)

true

(2)

evalb(diff(x, [`$`(x, 1/2)]) = 2*sqrt(x/Pi))

false

(3)

ShowSolution(diff(x, x^(1/2)))

Error, invalid input: diff received x^(1/2), which is not valid for its 2nd argument

 

fracdiff(x, x, 1/2)

2*x^(1/2)/Pi^(1/2)

(4)

ShowSolution(fracdiff(x, x, 1/2))

Error, (in Student:-Calculus1:-ShowSolution) input expression does not have any incomplete calculus operations

 

NULL


Download meme.mw

 

I am curious to know steps of integration for e^(t^3)*(cos(t))^3 as Maple found the answer correctly. So I wanted to know how it got to that solution. I applied the commands shown in document but unable to get steps. I want to know the reason for this and is it possible to get it work.
 

``

exp(t^2)*cos(t)^3

int(exp(t^2)*cos(t)^3, t)

-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t+3/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t+1/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t-1/2)-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t-3/2)

(1)

Student[Calculus1][IntTutor]()

eval(-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t+3/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t+1/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t-1/2)-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t-3/2), [t = 1])

-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2+I)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2+I)+((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2-I)+((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2-I)

(2)

evalf[10](-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2+I)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2+I)+((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2-I)+((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2-I))

.8154967124+0.*I

(3)

        
with(Student:-Calculus1):

 

 

Understand(Int, constant, constantmultiple, sum, difference)

ShowSolution(Int(exp(t^2)*cos(t)^3, t), maxsteps = 1000)

Error, (in Student:-Calculus1:-ShowSolution) unable to compute solution steps

 

NULL


 

Download e.mwe.mw

 

5_6190449716501677775.pdf

I ahve a signal y_a to which adding mu(t) doesn't seem to give any plot but error , what is missing here?.

And also in second k(x,t) pdf file I want the value of k(x,t) after I did the integration. When I type k(x,t) and hit enter it's not giving me the value of k(x,t) but returns k(x,t) as it is.K(x_t).pdf

pdf.mw
 

with(stats)

"f(x):=statevalf[pdf,normald[0,2*4.47]]  "

proc (x) options operator, arrow, function_assign; statevalf[pdf, normald[0, 2*4.47]] end proc

(1)

plot(f(x), -20 .. 20)

 

int(x*f(x), x)

.5000000000*x^2*statevalf[pdf, normald[0, 8.94]]

(2)

NULL


 

Download pdf.mw

Want to integrate x*f(x) where x is from -20..20, I am expecting a pure float number but getting symbols like statevalf_pdf in answer.

 

recurssion.mw

NULL

"f(x,t) :=(|Psi|)^(2)"

proc (x, t) options operator, arrow, function_assign; abs(Psi)^2 end proc

(1)

" a(t):=piecewise(0<= t<=1,1.5*t,1<= t<=2,1.5*(2-t))"

proc (t) options operator, arrow, function_assign; piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 1.5*(2-t)) end proc

(2)

" y[a](t):=piecewise(0<= t<=0.1,a(t),0.1<= t<=0.2,-a(t))"

proc (t) options operator, arrow, function_assign; piecewise(0 <= t and t <= .1, a(t), .1 <= t and t <= .2, -a(t)) end proc

(3)

"y(t):=y[a](t)+mu(t)"

proc (t) options operator, arrow, function_assign; y[a](t)+mu(t) end proc

(4)

"w(t):=&int;x(t)*f(x,t) &DifferentialD;x"

proc (t) options operator, arrow, function_assign; int(x(t)*f(x, t), x) end proc

(5)

" v(t):=y(t)-w(t)*w(t)"

proc (t) options operator, arrow, function_assign; y(t)-w(t)^2 end proc

(6)

NULL

diff(K(x, t), t) = beta*v(t)*f(x, t)

Error, (in y[a]) too many levels of recursion

 

"map(int, , t)"

Error, invalid function arguments

"map(int,,t)"

 

NULL

Here psi is a general wave function from schrodinger wave equation.

Download recurssion.mw

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